A priori estimates in Sobolev spaces for a class of hyperbolic operators in presence of transition

2019 ◽  
Vol 16 (02) ◽  
pp. 245-270 ◽  
Author(s):  
Annamaria Barbagallo ◽  
Vincenzo Esposito
Keyword(s):  
Sobolev Spaces ◽  
A Priori Estimates ◽  
A Priori ◽  
Second Order ◽  
Hyperbolic Operators ◽  
Priori Estimates ◽  
Euclidian Space ◽  
Global Nature

We establish several a priori estimates of local or global nature in Sobolev spaces with general exponent [Formula: see text] for a class of second-order hyperbolic operators with double characteristics in presence of a transition in a domain of the Euclidian space [Formula: see text].

scholarly journals The Cauchy–Neumann and Cauchy–Robin problems for a class of hyperbolic operators with double characteristics in presence of transition

2020 ◽  
Vol 11 (4) ◽  
pp. 1991-2022
Author(s):  
Annamaria Barbagallo ◽  
Vincenzo Esposito
Keyword(s):  
Sobolev Spaces ◽  
Existence And Uniqueness ◽  
A Priori Estimates ◽  
A Priori ◽  
Existence And Uniqueness Results ◽  
Mixed Problems ◽  
Uniqueness Results ◽  
Hyperbolic Operators ◽  
Priori Estimates

Abstract The mixed Cauchy–Neumann and Cauchy–Robin problems for a class of hyperbolic operators with double characteristics in presence of transition is investigated. Some a priori estimates in Sobolev spaces with negative indexes are proved. Subsequently, existence and uniqueness results for the mixed problems are obtained.

scholarly journals On the Cauchy problem for a class of hyperbolic operators with triple characteristics

2020 ◽  
Author(s):  
Annamaria Barbagallo ◽  
Vincenzo Esposito
Keyword(s):  
Cauchy Problem ◽  
Sobolev Spaces ◽  
Existence Result ◽  
A Priori Estimates ◽  
A Priori ◽  
Hyperbolic Operators ◽  
Priori Estimates ◽  
The Cauchy Problem

AbstractThe Cauchy problem for a class of hyperbolic operators with triple characteristics is analyzed. Some a priori estimates in Sobolev spaces with negative indexes are proved. Subsequently, an existence result for the Cauchy problem is obtained.

A priori estimates of solutions of nonlinear boundary value problems for singular in a phase variable second order differential inequalities

2014 ◽  
Vol 21 (2) ◽  
Author(s):  
Ivan Kiguradze
Keyword(s):  
A Priori Estimates ◽  
A Priori ◽  
Nonlocal Boundary ◽  
Nonlocal Boundary Conditions ◽  
Second Order ◽  
Phase Variable ◽  
Differential Inequalities ◽  
Nonlinear Boundary Value Problems ◽  
Estimates Of Solutions ◽  
Priori Estimates

Abstract.For singular in a phase variable second order differential inequalities, a priori estimates of positive solutions, satisfying nonlinear nonlocal boundary conditions, are established.

scholarly journals Periodic solutions for second order differential equations with indefinite singularities

2019 ◽  
Vol 9 (1) ◽  
pp. 994-1007 ◽  
Author(s):  
Shiping Lu ◽  
Xingchen Yu
Keyword(s):  
Differential Equations ◽  
Periodic Solutions ◽  
A Priori Estimates ◽  
A Priori ◽  
Second Order ◽  
Continuation Theorem ◽  
Second Order Differential Equations ◽  
Priori Estimates ◽  
Negative Constant

Abstract In this paper, the problem of periodic solutions is studied for second order differential equations with indefinite singularities $$\begin{array}{} \displaystyle x''(t)+ f(x(t))x'(t)+\varphi(t)x^m(t)-\frac{\alpha(t)}{x^\mu(t)}+\frac{\beta(t)}{x^y (t)}=0, \end{array}$$ where f ∈ C((0, +∞), ℝ) may have a singularity at the origin, the signs of φ and α are allowed to change, m is a non-negative constant, μ and y are positive constants. The approach is based on a continuation theorem of Manásevich and Mawhin with techniques of a priori estimates.

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